Method and system for calculating a flight route

ABSTRACT

The invention concerns a method and a system for calculating a flight route between a first position and a second position. According to the method, the first position is chosen as the current position, and the following steps are then repeated until the second position is reached: a loss function is determined corresponding to each flight path in a set of flight paths that are predefined in relation to the current direction of flight; a flight path that yields the most advantageous value for the loss function is selected; a subsection from the current position and a predetermined number of positions forward are registered for the selected flight path, and the position at the end of the subsection is chosen as the new current position.

TECHNICAL AREA

This invention concerns a method and a system for calculating a flightroute for an aircraft between a first position and a second position.

STATE OF THE ART

In the case of, e.g. reconnaissance or fighter missions, a mission planis normally prepared before the mission begins. At that time the pilotsplan their routes and input them into their aircraft computers. Theinput route is then displayed on a display unit arranged in theaircraft, whereupon the pilot can fly along the input route. Ifsomething unforeseen happens during the flight and compels the pilot todeviate from the input route, then the pilot must normally attempt toreturn to the input route as soon as possible.

It is not always feasible to return to the input route after an evasivemaneuver. For example, such a return might entail so large a detour thatthe fuel supply will not suffice. It can also be difficult to return tothe route because of impediments that lie in the way, e.g. in the formof hostile radar, extremely uneven terrain, etc. As a result, the needexists to be able to replan a mission while the mission is being carriedout.

Current studies have been made in which replanning solutions have beendeveloped wherein a new route is automatically generated during theflight. These studied solutions are however encumbered by thedisadvantage that the new routes can be calculated in only twodimensions, i.e. the route is assumed to be flown at constant altitude.This entails that these solutions cannot include the possibility thatthe terrain or threat can be flown over. As a result, the replannedroutes are characteristically long and, in turn, fuel-intensive.

SUMMARY OF THE INVENTION

One purpose of the invention is to provide an improved, vis-à-vis theknown art, means of calculating a flight route between a first positionand a second position in which threat exposure is taken into account,and which also enables calculation of the flight route both verticallyand horizontally.

This has been achieved in an embodiment by means of a method in whichthe first position is initially selected as the current position, andwherein the following steps are repeated until the second position isreached:

-   -   a loss function is determined corresponding to each flight path        in a set of flight paths that are of equal length and predefined        in relation to the current direction of flight;    -   a flight path that yields the most advantageous value for the        loss function is selected;    -   a subsection from the current position and a predetermined        number of positions forward is registered for the selected        flight path, and    -   the position at the end of the subsection is chosen as the        new-current position.

The method is intended for use in aircraft, e.g. fighter aircraft,reconnaissance aircraft and, unmanned aircraft. The method istime-discrete, so that the loss function for each tested flight path iscalculated as a sum of the “losses” for a number of calculatingpositions along the flight path. In one embodiment of the invention onlythe first calculating position is registered, whereupon it is given asthe new current position and the method is repeated as described above.

According to one embodiment of the invention, the flight paths in theflight path set are chosen based on a control signal sequence associatedwith each flight path. For technical reasons associated with thecalculating process, it is advantageous if the second through the finalsignal in each control signal sequence are zeroed.

The loss function preferably comprises one or more of the followingparameters a) a first parameter that indicates whether the tested flightpath crosses a pre-defined threat zones, b) a second parameter thatindicates whether the tested flight path passes too near to the terrain,c) a third parameter that indicates whether the tested flight pathexceeds a pre-defined altitude value, d) a fourth parameter thatindicates whether the tested flight path is costly from a fuelstandpoint, and e) a fifth parameter that indicates the distance to thesecond position of the route.

When necessary, the method can be supplemented with a refining step inwhich registered points located as far from one another as possible, butbetween which unobstructed visibility prevails, are marked asbreakpoints, and in which the route is selected as straight linesbetween these marked breakpoints.

The invention also comprises a system for realizing the foregoingmethod. The system comprises a terrain database arranged so as to storeterrain data, including latitude and longitude data with associatedaltitude data or the like; a threat database arranged so as to storedata concerning threats that includes at least data regarding thegeographic extent of the threats, and a first calculating unit that isoperatively connected with the terrain database and the threat databaseand arranged so as to calculate the route between the first and thesecond positions.

In cases where the system is also arranged so as to perform the refiningstep, the first calculating unit, the terrain database and the threatdatabase are operatively connected to a second calculating unit, whichis arranged so as to receive the flight route calculated by the firstcalculating unit and refine it, whereupon registered points that arelocated as far as possible from one another but between whichunobstructed visibility prevails are marked as breakpoints, and in sucha way that the route is selected as straight lines between these markedbreakpoints.

The method and system according to the invention enable the predictionof a three-dimensional route that takes an aircraft to an end point withminimized risk of entering the threat zones, and along which theaircraft can fly as low as possible without risk of colliding with theterrain. The method is also highly computation-efficient, and a routecan generally be planned in the course of several seconds.

BRIEF DESCRIPTION OF FIGURES

FIG. 1 shows a block diagram illustrating an example of a system formission planning, intended for aircraft.

FIG. 2 shows a flow diagram that illustrates the function of the firstcalculating unit in the system in FIG. 1.

FIG. 3 shows a flow diagram that illustrates the function of the secondcalculating unit in the system in FIG. 1.

FIG. 4 shows an example of the route predicted by the first calculatingunit and the refined route calculated by the second calculating unit.

PREFERRED EMBODIMENTS

Reference number 6 in FIG. 1 designates a system for calculating a routefor an aircraft between a start position and an end position. The system6 comprises a terrain database 1, a threat database 2, a firstcalculating unit 3 for calculating a preliminary route, a secondcalculating unit 4 for modifying the preliminary route, and a display 5.The system 6 can be built into the aircraft in its entirety.Alternatively, the entire system can be housed in a ground-based station(not shown), in which case data concerning the current position (startposition) of the aircraft and its final objective are communicated tothe ground-based station via a link, whereupon the ground-based stationcalculates a route and returns coordinates for that route to theaircraft. In yet another example, some parts of the system 6 arearranged at the ground-based station, while the rest are arranged in theaircraft. The aircraft consists of, e.g. a military reconnaissanceplane, a military fighter plan or an unmanned aircraft. In thedescription to follow, an unlimited example will be used in which theaircraft is an airplane.

The terrain database 1 stores terrain data for large land areas. In oneexample the terrain database 1 contains altitude data stored at 50 meterintervals along with associated latitude and longitude data or the like.The altitude values between these sampling points can be derived bybilinear interpolation. Threats are stored in the threat database 2.Each threat has a geographic position. A range is also linked to eachthreat. In an example where the threat is a radar station, a specificcoverage area is linked to the radar. The size and orientation of thecoverage area are determined by the power of the radar and how it isdirected. In another example the threat is a missile fired from a launchramp. The missile also has a geographical position and a range.

The first route-calculating unit 3 is connected to the terrain database1 and the threat database 2. The start state and end state are inputinto the calculating unit 3. The start state characteristically definesthe current position of the aircraft, i.e. its starting position, and isrepresented by, e.g. latitude, longitude and altitude. In this exemplaryembodiment the calculating unit 3 can be connected to a GPS receiverthat furnishes relevant latitude, longitude and altitude data. The endstate is defined as the final objective of the airplane, and isrepresented by e.g. an end position and bearing. The end position isspecified by, e.g. latitude, longitude and altitude. It is advantageousto include a bearing in the end state because the airplane usually hasto land at its final objective, whereupon the plane must approach thelanding strip from an angle that permits a landing to be made. The endstate is input via, e.g. an input device arranged in the cockpit.Alternatively, the end state data can be fed to the plane via a link forforwarding to the calculating unit 3. The calculating unit 3 calculatesthe preliminary route based on the input start state and end state data,and on the data in the terrain database and the threat database. Thepreliminary route is fed to the second calculating unit 4, which is alsoin communication with the terrain database 1 and the threat database 2.The second calculating unit 4 calculates the modified route based on theinput preliminary flight path and the data in the terrain database andthe threat database. The modified flight path is fed to the display 5for presentation. Presentation of the flight path can be achieved by,e.g. displaying the coordinate data or via a graphic illustration of theroute in the terrain. The modified route characteristically consists ofa number of breakpoints, specified in three dimensions, with straightflight paths between them.

In FIG. 3 the calculating unit 3 reads 7 first the start state and then8 the end state. In an example that is not shown, the start and endstates are read in reverse order. The calculating unit 3 then usesso-called MPC (Model Predictive Control) in a modified form as describedbelow to determine the preliminary route. Implementing the MPC algorithmrequires a state description for the system that is to be controlled.The state description for a non-linear model takes the general form:x(k+1)=f(x(k),u(k))u(k)εU

In a simple embodiment, a three-dimensional point-mass model withconstant speed is used. The direction of the speed vector of the pointcan be controlled by a control signal comprising a control signalcomponent u_(Θ) for conversion in the vertical plane and a controlsignal component u_(φ) for conversion in the horizontal plane. Inaccordance with this simple point-mass model, the following state vectorx(k+1) is used:

${x\left( {k + 1} \right)} = {\begin{pmatrix}{x_{1}\left( {k + 1} \right)} \\{x_{2}\left( {k + 1} \right)} \\{x_{3}\left( {k + 1} \right)} \\{x_{4}\left( {k + 1} \right)} \\{x_{5}\left( {k + 1} \right)}\end{pmatrix} = \begin{pmatrix}{{\theta\left( {k + 1} \right)} = {{\theta(k)} + {\theta_{0}{u_{\theta}(k)}}}} \\{{\varphi\left( {k + 1} \right)} = {{\varphi(k)} + {\varphi_{0}{u_{\varphi}(k)}}}} \\{{x\left( {k + 1} \right)} = {{x(k)} + {s_{0}\mspace{11mu}{\cos\left( {{\varphi(k)} + {\varphi_{0}{u_{\varphi}(k)}}} \right)}{\cos\left( {{\theta(k)} + {\theta_{0}{u_{\theta}(k)}}} \right)}}}} \\{{y\left( {k + 1} \right)} = {{y(k)} + {s_{0}\mspace{11mu}{\sin\left( {{\varphi(k)} + {\varphi_{0}{u_{\varphi}(k)}}} \right)}{\cos\left( {{\theta(k)} + {\theta_{0}{u_{\theta}(k)}}} \right)}}}} \\{{z\left( {k + 1} \right)} = {{z(k)} + {s_{0}\mspace{11mu}{\sin\left( {{\theta(k)} + {\theta_{0}{u_{\theta}(k)}}} \right)}}}}\end{pmatrix}}$

Note that the states x₃, x₄ and x₅ in the example shown represent theCartesian coordinates x, y and z, representing e.g. latitude, longitudeand altitude. Assuming that the speed is constant, it follows that go isa constant that denotes the distance that the aircraft is assumed tocover between two calculation points. s_(o) is thus a constant thatdepends on the flight speed and sampling interval. In one embodiment thesampling interval is chosen so that s_(o) is 200-300 m, e.g. 250 m.θ_(o) and φ_(o) are predefined angular constants, where θ_(o) indicatesan angle in the vertical plane and φ_(o) indicates an angle in thehorizontal plane. For example, θ_(o)=π/24 rad and φ_(o)=π12 rad. Tosimplify the subsequent calculations, it is assumed that the controlsignals u_(θ), u_(φ) can only assume a number of predefined values. Allstates in the state matrix are measurable.

In determining the preliminary route, a cost function is used in thenext step 9 in FIG. 2.

${J(k)} = {{\sum\limits_{j = k}^{k + N - 1}{{g^{T}\left( {j❘k} \right)}Q_{1}{g\left( {j❘k} \right)}}} + {Q_{2}{h\left( {j❘k} \right)}}}$where in one example g(j|k) and h(j|k) are chosen as follows:

$\begin{matrix}{{g\left( {j❘k} \right)} = \begin{bmatrix}\begin{matrix}{{x\left( {j❘k} \right)} - x_{end}} \\{{y\left( {j❘k} \right)} - y_{end}}\end{matrix} \\{{z\left( {j❘k} \right)} - z_{end}}\end{bmatrix}} \\{{h\left( {j❘k} \right)} = \begin{bmatrix}{{terr}\left( {{x\left( {j❘k} \right)},{y\left( {j❘k} \right)},{z\left( {j❘k} \right)}} \right)} \\{{threat}\left( {{x\left( {j❘k} \right)},{y\left( {j❘k} \right)},{z\left( {j❘k} \right)}} \right)} \\{{height}\left( {z\left( {j❘k} \right)} \right)} \\{{fuel}\left( {\theta\left( {j❘k} \right)} \right)}\end{bmatrix}}\end{matrix}$x_(end), y_(end) and z_(end) represent the coordinates for the end state(in the state matrix, the end states for x₃, x₄ and x₅), and thus hereperform the function of a constant reference signal. The functionsterr(x,y,z) and threat(x,y,z) yield the value 1 if the position x(j|k),y(j|k), z(j|k) determined from states x₃, x₄ and x₅ is located below theterrain or in a threat zone, while it yields the value 0 if such is notthe case. In an expanded embodiment, a determination is made as towhether, in the given case, the position lies in a threat zone ifso-called radar shadow prevails, i.e. whether there is a line of sightbetween the threat and the point, or if terrain is interposed. If radarshadow does prevail, then threat(x,y,z) will yield the value 0 even ifthe position is located in a threat zone. The function height(z) yieldsthe value 1 if the plane climbs above a predetermined altitude z_(max),and the value 0 if such is not the case. The predetermined altitudez_(max) is set so as to prevent the aircraft from flying unnecessarilyhigh, with the risk associated therewith, over as large an area aspossible. The function fuel(θ(j|k)) indicates the fuel consumption inaccordance with a simple model, e.g.:fuel(θ(j|k))=s ₀ e ^(c·θ(j|k))where c is a constant with a predefined value. At least when theairplane begins to approach its final objective, its bearing should alsobe included in the cost function if the plane is to go in for a landing.

The cost function J(k) is evaluated for a predefined prediction horizonN. For example, the prediction horizon is chosen so that the costfunction is minimized for a flight segment of 5-20 km. In one examplewhere s_(o)=250 m and N=50, the cost function is minimized for a flightsegment of 12.5 km. The flight segment that is evaluated ischaracteristically substantially shorter than the distance between thestart position and the end position.

When evaluating the cost function, a test is run to determine whichvalues the function yields for a number of predefined control signals xu_(Θ, u) _(ψ) whereupon the control signal u_(θ), u_(φ) that minimizesthe cost function is chosen. In one example U=(−3, −2, −1, 0, 1, 2, 3),in which example the control signal u_(θ), u_(φ) can assume 49 differentvalues ((−3, −3), (−3, −2) . . . ). To reduce the calculation load, acontrol signal horizon M is also set equal to 1. This means that onlythe first control signal prediction u(k|k) is optimized, the rest of thecontrol signals u(k+j|k), j=1, . . . , N−1 are given the value 0. Inthis way the cost function J(k) is evaluated along rays in a cone in thethree-dimensional space. Each ray represents a potential flight pathwhose length depends on the prediction horizon N and the samplinginterval. The number of flight paths for which the loss function iscalculated can be limited to further reduce the calculation load.

Q₁ and Q₂ in the cost function J(k) are weight matrices defined asfollows:Q₁=α1Q₂=[β₁ β₂ β₃ β₄]

The way in which the values in the weight matrices are to be chosen doesnot fall within the scope of this application, but generally speakingthe value of B₁, which determines the weight according to the plane notcrashing into the terrain is set very high, while B₂, which determinesthe weight accorded to the plane not flying into a threat zone isgenerally set to a lower value. For example, the value of B₂ can dependon the nature of the threat. The value of B₃, which indicates the weightaccorded to not flying too high, is also substantially lower than thevalue of B₁. On the other hand, the value of B₄, which indicates theweight accorded to not running out of fuel, is set so that the risk ofendangerment due to the fuel running out before the mission is completedis minimized.

To summarize, the control signal u_(Θ), u_(ψ) that minimizes the costfunction J(k) is determined in step 9. A flight path associated with thedetermined control signal is also derived. In a next step 10, thecoordinates x(k+1), y(k+1), z(k+1) that produced the lowest value ofJ(k) in step 9 are registered. If the distance between the positionx(k+1), y(k+1), z(k+1) and the end position x_(end), y_(end) and z_(end)exceeds the given distance d, a step 11 k=k+1 is added, whereupon theprocess is repeated from step 9.

The path vector that is input to the second calculating unit 4 consistsof a relatively large number, here designated R, of breakpoints, whereinthe distance between the breakpoints is s_(o). As noted above, s_(o) ischaracteristically 200-300 m. The second calculating unit is arranged soas to create a route consisting of a reduced number of breakpoints byfunctioning as per the scheme shown in FIG. 3.

In a first step 13, a determination is made as to whether a line ofsight exists between the start point (P₁=x(1), y(1), z(1) and the endpoint P₂=x(n=R), y(n=R), z(n=R). A line of sight is defined as thestraight line between two points that does not pass through terrain orthreat zones. If the line of sight is not unobstructed, then a pointcloser to the start point P₁ is chosen, whereupon a determination isagain made as to whether an unobstructed line of sight exists betweenthe points P₁ and P₂. This process is repeated until a point P₂ is foundwhere the line of sight to P₁ is unobstructed. In the example shown inthe figure, n is decreased 14 in single step increments, with adetermination being made each time as to whether an unobstructed line ofsight is present. It will be apparent to one skilled in the art thatmethods exist that may be more efficient than decreasing in single stepincrements from the end position when searching for the point P₂ that islocated farthest from P₁ but still offers an unobstructed line of sight.The invention must not be viewed as being limited to the method forfinding P₂ described herein.

Once an unobstructed line of sight between the point pair P₁, P₂ hasbeen found, the coordinates for the point pair are stored. If the pointP₂ does not coincide with the end point x_(end), y_(end) and z_(end) forthe mission, then the process is repeated in order to find a line ofsight between P₂ and a point P₃, where initially P₃=x(n=R), y(n=R),z(n=R). If there is no unobstructed line of sight between P₂ and P₃,then n is decreased in single step increments as above, whereupon adetermination is made as to whether an unobstructed line of sightexists. When a point P₃ is found that has an unobstructed line of sightto P₂ a determination 16 is made as to whether P₃ coincides with the endpoint for the mission. If such is not the case, the foregoing process isrepeated until all breakpoints P₁, P₂, etc. for the refined route arefound. The refined breakpoints P₁, P₂, etc. determined in the secondcalculating unit 4 are delivered 17 to the display 5.

Reference 20 in FIG. 4 designates the start position and reference 21the end position of the route. The preliminary route 18 calculated bythe first calculating unit 3 and the refined route 19 calculated by thesecond calculating unit 4 are marked between the start position 20 andthe end position 21. In addition to containing a limited number ofbreakpoints relative to the preliminary route, the refined route is alsoshorter than the preliminary route. This is attributable to the factthat the preliminary route is calculated using a limited predictionhorizon. The threat zones 22, 23 are thus not detected until they fallwithin the prediction horizon, so that the results lead, in certainsituations, to the preliminary route not being the shortest conceivableroute.

1. A method for calculating a flight route between a first position anda second position, wherein the first position is initially chosen as acurrent position, and wherein the following steps are repeated until thesecond position is reached: a loss function is determined correspondingto each flight path in a set of flight paths that are predefined inrelation to a current direction of flight; a flight path that yields amost advantageous value for the loss function is selected; a subsectionfrom the current position and a predetermined number of positionsforward are registered for the selected flight path; a position at anend of the subsection is chosen as a new current position; wherein afterthe flight route has been calculated between the first and the secondposition, the calculated route is refined in a refining step, in whichregistered points that are located as far from one another as possiblebut between which unobstructed visibility prevails are marked asbreakpoints, and in that the route is chosen as straight lines betweenthese marked breakpoints.
 2. A method according to claim 1, wherein theloss function includes at least a subset of the following parameters: afirst parameter that indicates whether the selected flight path crossespredefined threat zones; a second parameter that indicates whether theselected flight path passes too near to terrain; a third parameter thatindicates whether the selected flight path exceeds a predefined altitudevalue; a fourth parameter that indicates whether the selected flightpath is costly from a fuel standpoint; a fifth parameter that indicatesa distance to a second position of the route.
 3. A method according toclaim 1, wherein the flight paths in the flight path set are selectedbased on a control signal sequence belonging to each flight path.
 4. Amethod according to claim 3, wherein a second through a final signal ineach control signal sequence are zeroed.
 5. A method according to claim1, wherein the predetermined number of positions forward is one.
 6. Asystem for calculating a flight route for an aircraft between a firstposition and a second position, wherein the system comprises: a terraindatabase arranged so as to store terrain data, including latitude andlongitude data with associated altitude data; a threat database arrangedso as to store data concerning threats, including at least dataconcerning a geographical extent of the threats; a first calculatingunit that is operatively connected to the terrain database and thethreat database and arranged so as to calculate a route between thefirst and the second positions, whereupon the first calculating unitoperates according to a predetermined scheme, wherein the first positionis initially selected as a current position, and wherein the followingsteps are repeated until the second position is reached: a loss functionis determined corresponding to each flight path in a set of flight pathsthat are predefined in relation to a current direction of flight; aflight path that yields a most advantageous value for the loss functionis selected; a subsection from the current position and a predeterminednumber of positions forward are registered for the selected flight path,and a position at an end of the subsection is chosen as a new currentposition; and wherein the first calculating unit, the terrain databaseand the threat database are operatively connected to a secondcalculating unit, which is arranged so as to receive the flight routecalculated by the first calculating unit and refine it, whereuponregistered points that are located as far as possible from one another,but between which unobstructed visibility prevails, are marked asbreakpoints, and in that the route is chosen as straight lines betweenthese marked breakpoints.
 7. A system according to claim 6,characterized in that the entire system is implemented in the aircraft.8. A system according to claim 6, characterized in that the system ispartly implemented in the aircraft and partly in a ground-based station,whereupon data are communicated between the aircraft the ground-basedstation via a link.